admit a solution for any \(m\in \mathbb {N}\) .
Moreover, by [1]}
there exists \(\lambda _0>0\)  such that
\(\inf \limits _{(A,u)\in \mathcal {C},\,\,|A|=\mathtt {v}} \mathcal {F}(A,u)= \inf \limits _{(A,u)\in \mathcal {C}} \mathcal {F}^\lambda (A,u)= \lim \limits _{m\rightarrow \infty } \inf \limits _{(A,u)\in \mathcal {C}_m,\,\,|A|=\mathtt {v}} \mathcal {F}(A,u)\) 
